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Yes, I wrote that paper.


Good to know. Thank you :)


Still, I need to have some input on what benefits would accrue if the SOL were mathematically defined with near unlimited precision.


If c were a mathematical constant then I think that would be fantastic. It would quite potentially reveal why many aspects of the universe are what they are rather than seeming arbitrary. My understanding, however, is that the speed of light is a physical constant.


I'm assuming you're using the terms like they are established in these links:

Let's see... first thing that comes to mind is that if c were a mathematical constant it would probably explain why nature is invariant under Lorentz transforms rather than being invariant under Galilean transforms as that depends on c being finite rather than infinite. Like wikipedia says:


If [math]kappa , = , 0 ,,[/math] then we get the Galilean-Newtonian kinematics with the Galilean transformation...


If [math]kappa,[/math] is negative, then we set [math]c , = , frac{1}{sqrt{- kappa}} ,[/math] which becomes the invariant speed, the speed of light in vacuum...


Only experiment can answer the question which of the two possibilities, κ = 0 or κ < 0, is realized in our world.

Lorentz transformation--Derivation--From group postulates


Think of it like this, we usually know why [math]pi[/math] (a mathematical constant) is in the definition of a physical constant or physical law like the Coulomb constant or the Lorentz force law—it's because the surface area of a sphere of radius r is [math]4 pi r^2[/math] so that the intensity of radiation or power of a force is inversely proportional to that. That aspect of the Coulomb constant is a result of the mathematical properties of three dimensional space.


If the speed of light could be derived without the help of any physical measurement then I believe there would be many, many physical formula, laws, and constants that would suddenly make sense. Why, for example, is the proportionality constant between units of space and time or between units of mass and energy the particular value that it is? It would be awesome to know that.


Are you thinking that you can derive c without using physical constants that depend on measurement? With something like,

[math] displaystyle { c } = frac{1}{sqrt{mu_0 epsilon_0}} [/math]

you cannot know the value of both [math]mu_0[/math] and [math]epsilon_0[/math] (vacuum permeability and permittivity) without physically measuring at least one of them. The same is reportedly true of all known derivations of c.



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